Metrological scanning probe microscope

ABSTRACT

This invention relates to a metrological scanning probe microscope system combining an SPM which employs an optical lever arrangement to measure displacement of the probe indirectly with another SPM which measures the displacement of the probe directly through the use of an interferometric detection scheme.

This application claims priority from provisional No. 62/123,004, filedNov. 3, 2015, the entire contents of which are herewith incorporated byreference.

This is a continuation in part of Ser. No. 13/999,614, filed Mar. 12,2014, the entire contents of which are herewith incorporated byreference.

BACKGROUND OF THE INVENTION

Scanning probe devices such as the scanning Probe microscope (“SPM”) oratomic force microscope (“AFM”) can be used to obtain an image or otherinformation indicative of the features of a wide range of materials withmolecular and even atomic level resolution. In addition, AFMs and SPMsare capable of measuring forces accurately at the piconewton tomicronewton range, in a measurement mode known as a force-distance curveor force curve. As the demand for resolution has increased, requiringthe measurement of decreasingly smaller forces free of noise artifacts,the old generations of these devices are made obsolete. A demand forfaster results, requiring decreasingly smaller cantilevers, onlyreinforces this obsolescence. The preferable approach is a new devicethat addresses the central issue of measuring small forces with minimalnoise, while providing an array of modules optimizing the performance ofthe device when using small cantilevers or when doing specializedapplications such as optical techniques for biology, optical techniquesfor photochemical, photothermal, photovoltaic and other light inducedchanges to the cantilever or sample, nanoindentation andelectrochemistry.

For the sake of convenience, the current description focuses on systemsand techniques that may be realized in particular embodiments ofscanning probe devices, the SPM or the AFM. Scanning probe devices alsoinclude such instruments as 3D molecular force probe instruments,scanning tunneling microscopes (“STMs”), high-resolution profilometers(including mechanical stylus profilometers), surface modificationinstruments, nanoindenters, chemical/biological sensing probes,instruments for electrical measurements and micro-actuated devices. Thesystems and techniques described herein may be realized in such otherscanning probe devices.

A SPM or AFM is a device which obtains topographical information (andother sample characteristics) while scanning (e.g., rastering) a sharptip on the end of a probe relative to the surface of the sample. Theinformation and characteristics are obtained by detecting small changesin the deflection or oscillation of the probe (e.g., by detectingchanges in amplitude, deflection, phase, frequency, etc.) and usingfeedback to return the system to a reference state. By scanning the tiprelative to the sample, a map of the sample topography or othercharacteristics may be obtained.

Changes in the deflection or oscillation of the probe are typicallydetected by an optical lever arrangement whereby an incident light beamis directed onto the side of the probe opposite the tip and a reflectedbeam from the probe illuminates a position sensitive detector (“PSD”).As the deflection or oscillation of the probe changes, the position ofthe reflected spot on the PSD also changes, causing a change in theoutput from the PSD. Changes in the deflection or oscillation of theprobe are typically made to trigger a change in the vertical position ofthe base of the probe relative to the sample (referred to herein as achange in the Z position, where Z is generally orthogonal to the X/Yplane defined by the sample), in order to maintain the deflection oroscillation at a constant pre-set value. It is this feedback that istypically used to generate a SPM or AFM image.

It will be noted that the optical lever arrangement measures probemotion indirectly by measuring the angle of reflection of a light beamfrom the probe to the PSD. A few SPMs and AFMs, particularly earliermanifestations, have measured the motion of the probe directly throughthe use of an interferometric detection scheme. This method of measuringthe motion of the probe gives the user a direct measurement of probedisplacement and velocity.

SPMs or AFMs can be operated in a number of different samplecharacterization modes, including contact modes where the tip of theprobe is in constant contact with the sample surface, and AC modes wherethe tip makes no contact or only intermittent contact with the surface.

Actuators are commonly used in SPMs and AFMs, for example to raster theprobe or to change the position of the base of the probe relative to thesample surface. The purpose of actuators is to provide relative movementbetween different parts of the SPM or AFM: for example, between the tipof the probe and the sample. For different purposes and differentresults, it may be useful to actuate the sample or the tip or somecombination of both. Sensors are also commonly used in SPMs and AFMs.They are used to detect movement, position, or other attributes ofvarious components of the SPM or AFM, including movement created byactuators.

For the purposes of this specification, unless otherwise indicated, theterm “actuator” refers to a broad array of devices that convert inputsignals into physical motion, including piezo activated flexures; piezotubes; piezo stacks, blocks, bimorphs and unimorphs; linear motors;electrostrictive actuators; electrostatic motors; capacitive motors;voice coil actuators; and magnetostrictive actuators; and the term“sensor” or “position sensor” refers to a device that converts aphysical quantity such as displacement, velocity or acceleration intoone or more signals such as an electrical signal, including opticaldeflection detectors (including those referred to above as a PSD andthose described in U.S. Pat. No. 6,612,160, Apparatus and Method forIsolating and Measuring Movement in Metrology Apparatus); capacitivesensors; inductive sensors (including eddy current sensors);differential transformers (such as those described in U.S. Pat. No.7,038,443 and continuations thereof, Linear Variable DifferentialTransformers for High Precision Position Measurements; U.S. Pat. No.8,269,485 and continuations thereof, Linear Variable DifferentialTransformer with Digital Electronics; and U.S. Pat. No. 8,502,525, andcontinuations thereof, Integrated Micro-Actuator and Linear VariableDifferential Transformers for High Precision Position Measurements, eachof which is hereby incorporated by reference in their entirety);variable reluctance; optical interferometry; strain gages; piezosensors; and magnetostrictive and electrostrictive sensors.

Some current SPM/AFMs can take images up to 100 um², but are typicallyused in the 1-10 um² regime. Such images typically require from four toten minutes to acquire. Efforts are currently being made to move towardwhat has been called “video rate” imaging. Typically those who use thisterm include producing images at the rate of one per second all the wayto a true video rate at the rate of 30 per second. Video rate imagingwould enable imaging moving samples, imaging ephemeral events and simplycompleting imaging on a timelier basis. One important means for movingtoward video rate imaging is to decrease the mass of the probe, therebyachieving a higher resonant frequency while maintaining a lower springconstant.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1: A schematic of an optical beam positioning unit of the presentinvention optics used to form a focused light beam on the probe or thesample.

FIG. 2: Block diagram showing a light path of the present invention witha multiplicity of optical beam positioning units.

FIG. 3: Block diagram showing a light path of the present invention witha multiplicity of nested optical beam positioning units.

FIG. 4: Block diagram showing the Steering Mirror of an optical beampositioning unit and the Scheimpflug plane.

FIG. 5: Block diagram showing the Steering Mirror of an optical beampositioning unit and the Scheimpflug plane with the physical pivottranslated along the x-axis.

FIG. 6: Block diagram showing the Steering Mirror of an optical beampositioning unit and the Scheimpflug plane with the physical pivottranslated along the z-axis.

FIG. 7: Block diagram showing the Steering Mirror of an optical beampositioning unit and the Scheimpflug plane with the physical pivottranslated along the y-axis.

FIG. 8: Block diagram showing the Steering Mirror of an optical beampositioning unit and the Scheimpflug plane with the physical pivottranslated along the y-axis, z-axis and x-axis.

FIG. 9: Photographs showing cantilever response to being driven atdifferent frequencies and locations.

FIG. 10A is a Drawing of the ends of the optical paths of the SPM andthe LDV focused congruently onto a cantilever;

FIG. 10B is an Image of spots produced by the light beams on the side ofthe cantilever opposite the tip.

FIG. 11: Light paths of SPM and LDV with optical beam positioning unitfor each path.

FIG. 12: Light Path of SPM and LDV with single optical beam positioningunit.

FIGS. 13A, 13B and 13C: Effect of laser spot location on cantileverresponse.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

As already discussed the focused light beam in AFMs is used to measurethe deflection or oscillation of the probe. It is desirable however tofocus more than one light beam onto the probe to enable functionalitiesbeyond measuring probe displacement. It is also desirable to focus morethan one light beam onto the sample to enable other functionalities. Thepresent invention resolves the design complications that stem from sofocusing multiple light beams onto a single cantilever or the sample byoverlapping the multiple light beams along a single optical axis of asingle objective lens that is used to focus all the light beamscongruently. The angular orientation or direction of travel of eachlight beam and the axial position of the focus of each light beamrelative to the optical axis are controlled independently between lightbeams to allow for independent control of the three dimensional positionof the focus location of each light beam relative to the cantilever orsample.

FIG. 1 shows a schematic of the optical beam positioning (OBPU) unit ofthe present invention which forms one focused light beam on the probe orthe sample. Other focused light beams would employ a similar opticalbeam positioning unit. In FIG. 1 the light source 100 for the opticsemits a divergent beam of light that is substantially collimated by alens 104. The light source 100 could be a laser diode or another lightsource such as a superluminescent diode or light-emitting diode. Theonly requirement is that the power density be high enough to excite thedesired effect in the cantilever or the sample. The lens 104 ispreferably aspheric, in order to maximize the quality of the transmittedlight beam.

The collimated (or nearly collimated) light beam exiting the lens 104may optionally traverse a linear polarizer 108. The linear polarizer 108can be rotated about the optical axis relative to the light source 100(or the light source 100 may be rotated relative to the linear polarizer108) in order to maximize the light power throughput or to tune adesired amount of light throughput if the maximum amount of light poweris deemed excessive. Also, tilting the linear polarizer 108 relative tothe optical axis may be advantageous as it can reduce the amount ofback-reflected light returning into the light source 100. Back-reflectedlight may cause instabilities in the light emitting process.

The polarized light beam is subsequently passed through a lens 112 andrefocused. This lens may be an aspheric lens, achromatic doublet, orother lens or lens group. The light beam then reflects from a steeringmirror 116 that is disposed between the lens 112 and the focus of thelight beam 124. The steering mirror 116 is supported so that it can berotated about a physical pivot 120, defined as a point inthree-dimensional space. As will be shown below, rotation of thesteering mirror 116 about the physical pivot 120 provides a means formoving a focused spot in two dimensions in the plane of the probe or theplane of the sample. For the purposes of this specification these twoplanes are not shown separately in FIG. 1 but are collectively referredto herein as the target object 178.

The functioning of the steering mirror 116 is illustrated in detail inFIG. 4. In the preferred embodiment of the present invention, thesteering mirror 116 can be rotated about three orthogonal axes, two ofwhich are parallel to the mirror 116 surface and are important for thepurposes of the invention. The y-axis is one of the axes which isparallel to the mirror 116 surface. The y-axis lies within the plane 200defined by the incident light beam 204 and the reflected light beam 208.The z-axis is the other axis which is parallel to the mirror 116surface. The z-axis is orthogonal to the plane of incidence 200.Rotating the steering mirror 116 about the y-axis (“pitching” thesteering mirror 116) or about the z-axis (“yawing” the steering mirror116), or both, changes the direction and focus position of the reflectedlight beam 208. Rotating the steering mirror 116 about the x-axis(“rolling” the steering mirror 116) however has no effect on thedirection of the reflected light beam 208.

In the preferred embodiment, the steering mirror 116 is provided withmeans for actuating the pitch and yaw rotations in order to produce thedesired changes in the direction and focus of the reflected light beam208. This means may preferably be a kinematic stage driven bytransducers. The transducers and kinematic stage rotate the steeringmirror 116 in two dimensions about the physical pivot 120. Thesetransducers are preferably fine-pitch leadscrews driven byhigh-precision stepper motors. Alternately, the means of actuating thepitch and yaw rotations may be a rotary stage, flexure stage, or gimbalstage, and the transducers may be electromechanical motors, DC motors,piezoelectric inertial motors, piezoelectric transducers, or manualpositioners. Preferably, if the transducers are stepper motors, they areprovided with a gearbox to reduce the mechanical step size such that thepositioning of the light beam focus is precise.

Pitching and/or yawing the steering mirror 116 affects the reflectedlight beam 208 in two different ways. First, pitching and/or yawing thesteering mirror 116 affects the two-dimensional angular orientation ordirection of travel of the reflected light beam 208. Second, pitchingand/or yawing the steering mirror 116 affects the axial position of thefocus of the reflected light beam 208. If the physical pivot 120 (aboutwhich the steering mirror 116 can be rotated) is located at the point ofincidence 216 (where the incident light beam 204 intersects thereflected light beam 208), as drawn in FIG. 4, the effect ofpitching/yawing on the axial position of the focus is minimal. Only theangular orientation of the reflected light beam 208 is affected bypitching and/or yawing under this condition. However, if the physicalpivot 120 is translated relative to the point of incidence 216 as shownin FIG. 5, FIG. 6 and FIG. 7, pitching and/or yawing moves the axialposition of the focus of the reflected light beam 208 at the same timethat it changes the angular orientation of the reflected light beam 208.This is crucial to the present invention. When designing the opticalsystem, the exact location of the physical pivot 120 inthree-dimensional space is tuned to set a desired relationship betweenthe axial position of the focus and the angular orientation of thereflected light beam 208. When this relationship is achieved, the axialposition of the focus is geometrically constrained to move along amathematically defined surface, the “Scheimpflug surface” 124. For smallangular changes around the reflected light beam 208 the Scheimpflugsurface can be approximated by a “Scheimpflug plane” 212, as drawn inFIG. 4. The term Scheimpflug surface 124 refers to an optical principle,the Scheimpflug criterion, which is used to select the desiredScheimpflug plane 124 based on the planes of the target object 178.

As displayed in FIG. 4, translating the physical pivot 120 relative tothe point of incidence 216 along the x-axis has no consequence on theorientation of the Scheimpflug plane. With the physical pivot 120translated only along the x-axis, pitching and/or yawing the steeringmirror 116 moves the reflected light beam 208 along the same Scheimpflugplane as it would have moved prior to translation of the physical pivot120. Therefore, to understand the operation of the present invention, itsuffices to discuss the effect of rotating the steering mirror 116 aboutrotation axes that are in the plane of the mirror surface, intersectingin a physical pivot 120 that is also in the plane of the mirror surface.It may be noted however that placing the physical pivot 120 along thex-axis a short distance behind the plane of the steering mirror 116 haslittle effect on performance.

FIG. 5 illustrates the effect of translating the physical pivot 120along the z-axis: the Scheimpflug plane 212 is rotated due tosimultaneous changes in the axial position of focus and angularorientation of the reflected light beam 208. Specifically, theScheimpflug plane 212 is rotated (“tilted”) along an axis that liesparallel to the plane of incidence 200. The position of the focus movesalong a tilted focal plane as the steering mirror 116 is yawed orpitched about the physical pivot 120.

FIG. 6 illustrates the effect of translating the physical pivot 120along the y-axis: the Scheimpflug plane 212 is rotated (“tipped”) alongan axis that lies perpendicular to the plane of incidence 200. Now, theposition of the focus moves along a tipped focal plane as the steeringmirror 116 is yawed or pitched about the physical pivot 120.

FIG. 7 illustrates that translations along the z-axis, the y-axis andthe x-axis may be combined, with the Scheimpflug plane 212 both “tilted”along an axis that lies parallel to the plane of incidence 200 and“tipped” along an axis that lies perpendicular to the plane of incidence200.

The Scheimpflug surface 124 has an optical image near the front focalplane 174 of the objective lens 170, which is approximated by the“conjugate Scheimpflug focal plane” 180 as shown in FIG. 1. The tiltangle of the conjugate Scheimpflug focal plane 180 about the opticalaxis of the reflected beam 208 [FIGS. 4, 5, 6, 7] is preferably tuned tomatch the tilt angle of the target object 178. Typically, AFMcantilevers are tilted by an angle between 5 and 15 degrees. It ispreferred to position the physical pivot 120 location so as to induce atilt in the conjugate Scheimpflug focal plane 180 that substantiallymatches the tilt angle of the cantilever. This allows the movement ofthe focused beam position along the cantilever by pitching or yawing thesteering mirror 116 without the need to refocus the light beam, whichwould otherwise be required for the tilted cantilever.

In an alternative embodiment of this invention, translation of thegoniometric lens group 136 may be used to compensate for the tilt angleof the cantilever. However, such an embodiment requires the use ofthree, instead of only two, motion transducers in order to retain afocused light spot on a tilted cantilever.

As depicted in FIG. 1, the light beam reflected from the steering mirror116 converges to a focus at the Scheimpflug surface 124 and subsequentlydiverges beyond that surface. The diverging light beam is thenredirected by reflection off a fold beamsplitter 128. The foldbeamsplitter 128 reflects part of the light beam, while allowing anotherpart to traverse through the fold beamsplitter 128 to a photodetector132 which measures the total amount of optical power in the light beam.The photodetector 132 can thus be used to tune the desired amount oflight power by changing the drive current of the laser diode 100accordingly or, as previously discussed, by rotating the linearpolarizer 108 accordingly. Typically, a small fraction of the light beamwill be allowed to traverse through the fold beamsplitter 128 to thephotodetector 132 and substantially all the light will be reflected fromthe fold beamsplitter 128. This division of the light beam is preferableas it maintains a high optical power density at the target object 178.

The photodetector 132 discussed in the previous paragraph may be alinear position-sensitive detector, in which case the position of lightbeam on the photodetector 132 can be used to determine the axialposition of the focus and the angular orientation of the light beam. Acalibration procedure may also suffice to determine these two geometricfactors. However a linear position-sensitive detector is desirablebecause it obviates the need for closed-loop position control on theactuators that produce pitch and yaw in the steering mirror 116. Howeverif closed-loop position control is in any event provided, a linearposition-sensitive detector complements such control and provides areinforcing measure of the nominal position or center position of thesteering mirror 116.

In the absence of a photodetector 132, which is optional and notrequired for the functioning of the present invention, the foldbeamsplitter 128 only acts as a mirror redirecting the light. With adifferent orientation and position of the optical components, the foldbeamsplitter 128 may not be necessary.

After reflecting from the fold beamsplitter 128, the light beamtraverses one or a number of lenses that substantially collimate thebeam. This group of lenses 136 is referred to herein as the goniometriclens group. The number and kind of lenses used to collimate the lightbeam depends on the exact optical parameters of the particular opticalbeam positioning unit under consideration as known to those skilled inthe art. In the present invention the goniometric lens group 136 isprovided with a means for translating the group along the optical axisto change the degree of collimation of the outgoing light beam. Movingthe group backward or forward causes the light beam to be more divergentor convergent after traversing the group. This allows a user to adjustthe axial position of the final focused spot relative to the targetobject 178.

One possible means of translating the goniometric lens group 136 is bymounting the lens group in a threaded housing that is then rotated in athreaded bore. The mechanical motion of the lens group may be automatedvia a transducer, such as a motor, or manually adjusted by the user. Thenumber of lenses in the group that may be required to move depends onthe desired amount of collimation. The remainder of the lenses in thegroup, if any, may remain fixed.

The substantially collimated beam exiting the goniometric lens group 136can be attenuated, if necessary, by the use of a filter 140 thatattenuates the light by a prescribed amount. The filter 140 may be aneutral density filter, a rotationally variable neutral density filter,a colored filter, or a linear polarizing filter. In any case, the filter140 can be adjusted manually by the user or through an automatedmechanism to change the desired amount of light attenuation. Preferableautomated mechanisms for this purpose include a rotationally variableneutral density filter on a motorized rotation stage and a motorizedfilter wheel with a plurality of filters, one of which is disposed inthe beam. If filter 140 is a linear polarizing filter, either the filteror the polarizer can be rotated either manually or by some motorizedmechanism. In any case it is preferable to electronically identifywhich, if any, filter 140 is disposed in the light beam so that theresulting beam power may be readily available.

The light beam emerging from the filter 140 then traverses a polarizingbeamsplitter 144 which passes only one polarization direction of thebeam. The portion of the beam that is polarized in the orthogonaldirection to the desired polarization direction is reflected, ratherthan transmitted, and then absorbed by a beam dump 148, such as a blackfelt surface. The portion of the beam that is polarized in the desiredpolarization direction is transmitted to a quarter-wave plate 152 whichconverts the linearly polarized light beam transmitted into a circularlypolarized light beam.

Optical elements in the path of the light beam after it exits thequarter-wave plate 152, such as the dichroic mirror 156, may introducesignificant phase shifts between s-polarized and p-polarized light inthe circularly polarized light beam. In this situation, the desiredoperation of the polarizing beamsplitter 144 and quarter wave plate 152can be achieved by replacing the quarter wave plate 152 with a waveplatehaving sufficient retardance (greater or less than 0.25 waves) withsuitable orientation so as to cancel the cumulative phase shiftintroduced by all subsequent optical elements in the light beam.

As noted above, the present invention may be used to measure thedeflection or oscillation of the probe as is common with AFMs and mayalso be employed to focus more than one light beam onto the probe (orthe sample) to enable functionalities other than measuring probedisplacement. When the present invention is used to achieve these otherfunctionalities, detection of the reflected beam from the probe orsample is not required. In this case, polarizing beamsplitter 144,waveplate 152 and beam stop 148, may be omitted without substantiallychanging the other aspects of the invention, and of course so also maythe photodetector 182 used to measure the deflection or oscillation ofthe probe. In this connection it is necessary to remember that thepresence or absence of the polarizing beamsplitter 144 and waveplate 152have an important effect on the calculation of the correct distances inlocating the virtual pivot 122 in the back focal plane 172 of objectivelens 170.

Substantially all the circularly polarized light beam transmitted fromthe quarter-wave plate 152 is reflected from a dichroic mirror 156. Anyportion of the beam that may traverse the dichroic mirror 156 isabsorbed by a beam dump 160. A dichroic mirror is used here rather thana conventional mirror so that wavelengths other than the wavelengths inlight source 100 will traverse the mirror 156 rather than beingreflected, thereby allowing the camera system 186 to image lightreflected from the target object 178.

The substantially collimated light beam exiting the dichroic mirror 156then traverses another dichroic mirror 166, which allows for a lightbeam from another optical beam positioning unit to be combined into thelight path, as will be described in more detail shortly. The collimatedlight beam then passes through an objective lens 170 that focuses thelight beam close to the front focal plane 174 of the objective lens 170.The target object 178 targeted by the focused light beam is locatedclose to the front focal plane 174 of the objective lens 170. Theobjective lens 170 may be a commercially available unit, such as theOlympus LUC Plan Fluor N 20x having a numerical aperture of 0.45, or itmay be an objective lens designed specifically for use in this context.Typically, an objective lens for use in this context is composed ofseveral optical components, some of which may be translated with respectto others to adjust the position of the front focal plane relative tothe position of the lens, or to adjust the spherical aberrationcorrection of the focused spot. The preferred lens will haveapochromatic or semi-apochromatic (“Fluor”) correction of chromaticaberrations because it may be anticipated that multiple light beams ofdifferent wavelengths producing a plurality of spots will be present.The preferred lens will also have flat field (“Plan”) correction foroff-axis aberrations because the camera system 186 will preferablyincorporate a digital image sensor, and because it may be anticipatedthat the invention will be used in conjunction with planar samples suchas silicon wafers.

Some portion of the light beam focused by the objective lens 170 closeto the front focal plane 174 of the lens will be reflected by the targetobject 178 also located close to the front focal plane 174. Anotherportion will be absorbed. It is also possible that some portion of thelight beam will be transmitted through the target object 178, dependingon the material and thickness of the target object 178, and thewavelength of the light beam.

Some portion of the light beam reflected by the target object 178 willre-enter the objective lens 170 and return to a substantially collimatedstate. The portion of the beam that re-enters the objective lens 170 maybe maximized by laterally offsetting the incoming collimated beam inorder to introduce a specific angle to the focused light beam, asdescribed in detail in U.S. Pat. No. 8,370,960, Modular Atomic ForceMicroscope, referred to above and incorporated herein by reference. Asubstantial part, but not all, of the reflected light beam thatre-enters the objective lens 170 reflects off the dichroic mirror 156and is directed to the quarter-wave plate 152 which then converts thecircularly polarized returning light beam into a linearly polarizedlight beam. Because the polarization orientation is now orthogonal tothe polarization orientation of the original light beam that previouslycrossed the quarter-wave plate 152 in the other direction, the lightbeam reflects off the polarizing beamsplitter 144 instead of traversingit. In the event that the quarter-wave plate 152 has been replaced by awaveplate having retardance and orientation to compensate for phaseshifts in optical elements coming after the quarter-wave plate 152, asdiscussed above, the returning light beam reflects entirely off thepolarizing beamsplitter 144.

The reflected beam then impinges on a photodetector 182 which, when thepresent invention is being used to measure the deflection or oscillationof the probe, measures the position of the light beam. Thetwo-dimensional position of the light beam on the photodetector 182 isused as a measure of the two-dimensional angular deviation of the targetobject 178 that reflected the light beam. However, when the presentinvention is employed to focus more than one light beam onto the probe(or the sample) to enable functionalities other than measuring probedisplacement, the photodetector 182 can be used to measure the lightpower of the light beam.

A portion of the light beam that re-enters the objective lens 170 willtraverse the dichroic mirror 156 and can be imaged using the camerasystem 186 if the target object 178 is illuminated by an appropriatelight source, preferably a white light source. The camera system 186 canalso image the focused light spot reflected from the target object 178.

In order to assure that the brightness of the target object 178 issimilar in magnitude to the brightness of the reflected light beamentering the camera system 186, a color filter 190 can be used toselectively dim the light beam to any degree necessary. It may also benecessary to adjust the exposure time and aperture size provided by thecamera system 186 to obtain proper exposure of the target object 178 andfocused light spot. Even if only a small amount of the reflected lightbeam traverses the dichroic mirror 156 to the camera system 186 the beamwill appear very bright due to its high power density. Therefore, it isanticipated that the filter 190 will be necessary to provide a goodquality image in the camera system 186.

As described earlier, translating the goniometric lens group 136 alongits axis changes the axial location of the final focused spot relativeto the front focal plane 174 of the objective lens 170. Prior art wouldhave positioned the light beam focus in the axial direction by eithermoving the objective lens 170, or moving the target object 178, or both.The present invention allows the light beam to be focused without movingthe objective lens 170 or the target object 178. The same will be truefor the light beam from another optical beam position unit (or units),with their own goniometric lens groups 136. The light beams of suchother units would enter the light path via other dichroic mirrorslocated between the dichroic mirror 156 of the first optical beampositioning unit and the objective lens 170. FIG. 1 shows one suchdichroic mirror 166. FIG. 2 shows a light path with a multiplicity ofoptical beam position units and dichroic mirrors. The additionaldichroic mirrors, starting with dichroic mirror 166, may have differentoptical specifications than dichroic mirror 156 in order to optimallycombine different light beams while minimizing loss of light power. Whenthe goniometric lens group 136 of any one of such units is translatedthe axial location of the final focused spot of the relevant unitrelative to the front focal plane 174 of the objective lens 170 ischanged without either moving the objective lens 170, or moving thetarget object 178, or both. This is a significant difference relative toprior art because moving the objective lens 170, or moving the targetobject 178, or both, in order to position the light beam focus in theaxial direction for the benefit of one optical beam positioning unitcould significantly degrade the performance of other optical beampositioning units. FIG. 3 shows another variation of the FIG. 2arrangement with multiplicity of optical beam position units feedinginto a single light path. In FIG. 3 two or more optical beam positionunits have their translational degrees of freedom coupled so that theirrespective focused light spots move together in a desired direction. Forexample, a secondary optical beam position unit may be tethered to aprimary optical beam position unit so that their focused light spotsmove together when the focused light spot of the primary optical beamposition unit is translated in one or more directions, while the focusedlight spot of secondary optical beam position unit is also moved focusedindependently relative to the focused light spot of the primary opticalbeam position unit. Although FIG. 3 represents three nested optical beamposition units, any number of degrees of freedom between any number ofoptical beam position units may be coupled as preferred by the user.

Metrological SPM

A metrological SPM or AFM may be created by combining an SPM or AFMwhich employs an optical lever arrangement to measure displacement ofthe probe indirectly with another SPM or AFM which measures thedisplacement of the probe directly through the use of an interferometricdetection scheme.

The inventors have used a SPM (the Cypher SPM from Asylum Research ofSanta Barbara, Calif.) and a quantitative laser doppler vibrometer (LDV)(the Laser Doppler Vibrometer from Polytec of Waldbronn, Germany) forsuch a metrological SPM. The instrument allows normal SPM operation withthe SPM optical lever arrangement while simultaneously allowingNIST-traceable measurements of the displacement and velocity of theprobe with the LDV system. The inventors are building on the presentinvention by combining two optical beam position units into themetrological SPM, one unit for the optical lever arrangement of the SPMand the other unit for interferometer of the LDV.

Panel (a) of FIG. 10 shows side views of the end of the optical path ofthe Cypher SPM and the end of the optical path of the LDV focusedcongruently onto a cantilever. Panel (b) of FIG. 10 shows the spotsproduced by the light beams on the side of the cantilever opposite thetip. The rectangular spot was produced by the SPM and the circular spotby the LDV. Both spots can be separately positioned and focused, ormoved together relative to the cantilever frame of reference. By virtueof its large numerical aperture, the LDV spot can be focused down to ˜2microns. This allows high-resolution mapping of the cantilever dynamics.Unlike sensitivity with the optical lever method, LDV sensitivity is notaffected by the reduction of spot size. More importantly, because theLDV measurement is encoded as a frequency (doppler) shift of a HeNelaser, the sensitivity is highly accurate and does not change with theoptical properties of the cantilever nor with laser power.

FIG. 11 shows the principal features of the two light paths of the twocomponents of the Metrological SPM. The light path of the SPM of thepresent invention is shown in greater detail in FIG. 1 discussed above,but the features of importance for the light path of the SPM in theMetrological SPM are identified on the right of FIG. 11. The light pathon the right of FIG. 11 has a light source 300 (and other components ofthe light path discussed below) as does the light path of FIG. 1, lightsource 100, but light source 300 is identified as an infrared laserwhile light source 100 is identified as a laser diode or other lightsource. The other components of the light path of FIG. 1 included inlight source 300 but not specifically identified are a polarizingbeamsplitter, quarter wave plate and photodetector (respectivelyidentified as items 128, 152 and 182 in the light path of FIG. 1). Theother components of the light path of FIG. 1, particularly the steeringmirror 116 and associated hardware that makes use of the steeringmirror, are not included in the light path on the right of FIG. 11.

The features of importance for the light path of the LDV in theMetrological SPM are identified on the left of FIG. 11. The light pathof the LDV starts with the laser doppler vibrometer 301. For thepurposes of the metrological SPM, a substantial portion of the laserlight produced in the LDV 301 is directed to a red dichroic mirror 302.The remainder of the laser light so produced (not shown) is used for thesecond beam required for the device to function as an interferometer(not shown).

The light from the infrared laser 300 in the light path on the right ofFIG. 11 is reflected by an infrared dichroic window 303 in the directionof the objective lens 170. This lens is substantially the same lens asthe objective lens of FIG. 1.

Much of the laser light directed to the red dichroic mirror 302 in thelight path on the left of FIG. 11 is reflected by the mirror and passesthrough the infrared dichroic window 303 in the direction of theobjective lens 170.

After having passed through the objective lens 170 the light from theinfrared laser 300 in the light path on the right of FIG. 11 reaches thetarget object 178 (which includes the cantilever plane) and is reflectedby the target object 178 back through the objective lens 170 andthereafter is reflected by the infrared dichroic window 303 to thephotodetector (which as already noted is included in light source 300)in order to carry out the traditional optical lever measurements of theposition of the light beam on the probe and the probe's deflection oroscillation.

of the position of the light beam on the probe and the its deflection oroscillation.

After having passed through the objective lens 170 the laser light fromthe infrared dichroic window 303 in the light path on the left of FIG.11 reaches the target object 178 (which includes the cantilever plane)and is reflected by the target object 178 back through the objectivelens 170 and thereafter through the infrared dichroic window 303 to thered dichroic mirror 302 from which it is reflected to the LDV where itis combined with the second beam (not shown) generated by the LDV inorder to measure interferometrically the objects of interest.

A second approach to a Metrological SPM is shown in FIG. 12. Here theinventors use only the quantitative laser doppler vibrometer (LDV) usedin the previous Metrological SPM. This approach also allows normal SPMoperation, equivalent to that with the Cypher SPM optical leverarrangement, while simultaneously allowing accurate NIST-traceablemeasurements of displacement and velocity of the probe. As with thefirst Metrological SPM the inventors are taking advantage of the presentinvention and using the optical beam position unit technology, but hereonly one such unit is required even though the functionality of both anoptical lever arrangement and an interferometer are provided.

The features of importance for this second approach are shown in thelight path of the Metrological SPM in FIG. 12. The light path startswith the laser doppler vibrometer 301. As with the first approach to aMetrological SPM, a substantial portion of the laser light from the LDV301 is directed to a red dichroic mirror 302. The remainder of the laserlight so produced (not shown) is used for the second beam required forthe device to function as an interferometer (not shown).

Much of the laser light directed to the red dichroic mirror 302 isreflected by the mirror and about half of this light passes through thebeamsplitter 304 in the direction of the objective lens 170. The otherhalf is absorbed by the beam dump 182.

After having passed through the objective lens 170 the laser light fromthe beamsplitter 304 reaches the target object 178 (which includes thecantilever plane) and is reflected by the target object 178 back throughthe objective lens 170 and thereafter about half of the laser lightexiting the objective lens 170 passes through the beamsplitter 304 andreaches the red dichroic mirror 302 from which it is reflected to theLDV where it is combined with the second beam (not shown) generated bythe LDV in order to measure interferometrically the objects of interest.

The other half of the laser light exiting the objective lens 170 isdirected by the beamsplitter 304 to the photodetector 148 in order tocarry out the traditional optical lever measurements of the position ofthe light beam on the probe and the probe's deflection or oscillation.

Piezoresponse Force Micoscopy (PFM) and Metrological SPM

PFM is based on the converse piezoelectric effect. After putting thecantilever tip in contact with a piezoelectric sample, the tip-samplebias voltage is modulated periodically. This generates an oscillatingelectric field below the tip and leads to localized deformations in thesample surface. The resulting sample vibrations act as a mechanicaldrive for the cantilever tip. The magnitude of effective piezoelectricresponse of the surface d_(eff), in pm/V, is measured as the amplitudeof the tip displacement divided by the amplitude of the tip-samplevoltage. In addition, the phase of the response provides informationabout the polarization direction.

It is well known that the drive frequency of the electrical excitationcan have a profound effect on the measured signal. Since the frequencyresponse of most ferroelectric samples should be flat into the GHzrange, this suggests that some features in the frequency response intothe MHz range may originate from cantilever dynamics instead offerroelectric effects. In order to minimize the effects of cantileverresonances on the ferroelectric signal, single-frequency PFM has mostlybeen limited to operation at a few hundred kHz or lower, with someexceptions. Two- or multiple-frequency techniques such as dual ACresonance tracking (DART) and band excitation (BE) have reduced theseverity of the problem by tracking the resonance frequency, but to alimited degree.

In addition, there are other forces present that respond to tip-samplebias modulation at any drive frequency, such as delocalizedelectrostatic forces between the body of the cantilever and the samplesurface charge. In many cases, the undesirable response of thecantilever to these electrostatic forces overwhelms the PFM signal ofinterest. Over the years, a number of approaches for maximizing the PFMresponse and minimizing or eliminating the electrostatic components havebeen developed; however, this issue remains a significant challenge.Misinterpreting the electrostatic signal as a tip displacement can leadto incorrect estimation of the piezoelectric sensitivity and relativephase response.

Positioning the LDV spot in different locations on the cantileverrelative to the tip location allows direct investigation of thecantilever dynamics that occur in PFM experiments. FIG. 13(a)illustrates three distinct scenarios: the laser spot is located oneither side of the tip, or directly above the tip. FIG. 13(b) shows theevolution of the system transfer function as the LDV spot is moved alongthe length of cantilever. As the laser spot is moved towards the end ofthe cantilever, an anti-resonance sweeps upward in frequency around thecontact resonance peak. When the LDV spot is located immediately abovethe tip (black curve), the resonance and anti-resonance pair cancels outand leads to a nearly flat response. In this specific location, the LDVsignal is blind to the dynamics of the cantilever and reports only thedisplacement of the tip, as can be understood by inspection of FIG.13(a). This situation is ideal for quantifying surface strain.

FIG. 13(c) demonstrates how the LDV spot location affects the measuredresponse. Although the images were acquired at a drive frequency of 25kHz, well below the contact resonance frequency of 380 kHz, thecantilever dynamics still have significant impact on the measured valuesof d_(eff) between different domains. In this scenario, the LDVmeasurement couples both the tip displacement and the cantileverdynamics. As explained in the previous paragraph, it is only when thelaser spot is directly above the tip that the measurement is decoupledfrom the cantilever dynamics.

These results suggest a methodology for accurately quantifying theelectromechanical response of a sample. Once tip-sample contact isestablished with a chosen OBD deflection setpoint, the contact resonancefrequency is identified by electrically driving the cantilever. Then,the LDV spot position is optimized by iterative minimization of themeasured frequency response around the resonance frequency. Finally,after achieving a flat frequency response around the contact resonance,conventional sub-resonant electromechanical imaging can be performedwith much higher accuracy. This protocol greatly extends the availablefrequency range for accurate PFM measurements, which is now limited onlyby the precision in positioning the LDV laser spot directly above thecantilever tip.

Photothermal Excitation

In addition to being used to measure the deflection or oscillation ofthe probe, the light beam of an optical beam positioning unit can beused to photothermally excite mechanical vibrations of the probe. Forthis purpose light at the blue end of the visible spectrum is preferred.The inventors have used the beam from a laser emitting light with a wavelength of 405 nm with satisfactory results.

In the prior art, a coating on some or all of the cantilever portion ofthe probe was required to convert heat from the light beam intomechanical strain in the probe, via different thermal expansioncoefficients of the coated portion of the cantilever and the remainderof the probe. While the current invention is compatible with such coatedcantilevers, it does not require a coating to photothermally inducemechanical vibrations of the probe. Due to the well-corrected opticaldesign, the light beam focus in the present invention is significantlysmaller than in the prior art. The smaller light beam focus produceslarger thermal gradients that cause photothermal excitation even inprobes fabricated from a single material. Because the material of theprobe has nonzero thermal expansion, the thermal gradients producestrain gradients, especially when the light beam power is modulated toproduce time-varying temperature gradients. For example, the light beampower can be changed sinusoidally as a function of time, producing asinusoidal mechanical motion as required for amplitude-modulated atomicforce microscopy. As described in prior art, such mechanical motion orvibration may also be enhanced by differences in thermal coefficients ofexpansion of two or more materials composing the probe in the case ofheterogeneous probes.

Photothermal excitation of the probe may also be used in conjunctionwith other methods to form hybrid modes of cantilever excitation. Forexample, the cantilever may be driven by piezoacoustic excitation at afirst resonance while simultaneously driven by photothermal excitationat a second resonance. This combination is useful if a large amplitudeof oscillation, achievable with piezoacoustic excitation, is necessaryfor a first resonance, while the clean response of photothermalexcitation is preferable for driving a second resonance. Alternativeschemes for excitation may be developed to meet specific experimentalgoals. For example, photothermal excitation could be used to excitemechanical motion at a resonance of the cantilever while piezoacousticexcitation is used to drive the cantilever at a frequency that is notclose to a cantilever resonance. Some of these schemes of excitation mayinvolve frequency modulation or frequency tracking, in order to measuremechanical parameters of the sample, the probe or the tip of the probe.In this case, photothermal excitation is known in the prior art toprovide an advantage because it provides a transfer function fromexcitation voltage to mechanical motion that is substantiallyindependent of frequency and free from spurious resonances.

The location of the focused light beam on the probe used forphotothermal excitation affects the drive amplitude of the probe. Therelationship between location and drive amplitude is also frequencydependent because the probe has a frequency response composed of manynormal and torsional eigenmodes. There are locations that provide zeroexcitation of the second eigenmode, while providing non-zero excitationof the first eigenmode, for example. Depending on the experiment, it maybe desirable to tune the drive amplitude of the probe at differentfrequencies. This may be achieved by modulating the power of thephotothermal excitation light beam at particular frequencies, that maycorrespond to different eigenmodes of the probe, while rastering thefocused spot relative to the probe and measuring the driven amplitude.It may be desirable, for example, to maximize the torsional (or normal)vibration response of the probe, while minimizing the response of thenormal (or torsional) deflection of the probe in certain experiments.

FIG. 9 shows an amplitude map of an ArrrowUHFAuD cantilever as afunction of blue laser excitation near the probe. The amplitude responseis also function of the modulation frequency of the blue light power.Modulating the light power at frequencies near the 1^(st) eigenmode and2^(nd) eigenmode of the probe, as shown in both images, inducesdifferent bending modes of the cantilever which have differentlocation-dependent responses. The width and height of each map is 66microns. The outline of the cantilever is also drawn for reference.

blueTherm

The light beam of an optical beam positioning unit can also be used toheat certain parts of the target object 178 to a varying degree. Forthis purpose light at the blue end of the visible spectrum is preferred.The inventors have used the beam from a laser emitting light with a wavelength of 405 nm with satisfactory results.

Heating certain parts of the target object 178 to a varying degreecauses a desirable steady-state temperature gradient to form in theprobe or the sample at time scales that are longer than the mechanicaltime constant of the object being heated. Such a steady-statetemperature gradient may occur while vibrations of the target object 178are being induced by modulating the light beam at faster time scales. Inany case, with the probe the temperature gradient can be optimized byadjusting the total optical power of the light beam and the beamposition relative to the probe to control the temperature of a certainpart of the probe, such as the tip of the cantilever. The variabletemperature of the probe and the tip of the cantilever can be used toinduce thermally activated changes in the sample according to anydesired experimental protocol. One category of such experiments is knownas local thermal analysis. In the prior art it is carried out using aspecial probe with heating elements and even a thermometermicrofabricated in the probe. Such special probes are costly and areonly available in a few spring constant values. With the presentinvention however such special probes are unnecessary as the focusedlight beam of the optical beam positioning unit can heat any existingprobe useful for a local thermal analysis experiment.

Although the present invention can photothermally excite mechanicalmotion in uncoated probes, it may still be beneficial to optimize theoptical and thermal properties of the probe for heating with the lightbeam of an optical beam positioning unit. For example, the reflectivityof the coating of the probe may be tuned appropriately, and the thermalconductivity of the probe may be patterned, through selective doping, inorder to allow heat to flow to the tip of the cantilever more readilythan to flow to the base of the probe (or vice versa). Furthermore, theprobe may be shaped in order to facilitate conduction of heat to the tipof the cantilever; for example, the tip of the cantilever may be hollowsuch that the incident beam is absorbed closer to the tip. Patterning ametallic coating on the probe or the tip of the cantilever may also beused to maximize the heat flow to the tip to attain higher tiptemperatures for a given light power. Coating only the end of the probenear the tip, while keeping the bulk of the probe uncoated, may also bebeneficial by reducing unwanted bending of the probe caused by thermalexpansion coefficient differences between the coating material and theprobe material.

It is beneficial to measure the temperature of the probe for severaltypes of experiments, such as calibrating the spring constant based onthermomechanical motion. In the present invention, the temperature ofthe probe may be quantified by measuring the change in the resonantfrequency of the probe while changing the power of the light beam, byturning the light beam on and off for example. The temperature of theprobe is related to its resonant frequency because Young's modulus ofthe probe is dependent on the temperature of the probe. Furthermore, theresidual stress in coated probe may have a temperature dependence thatcan impact the relationship between the resonant frequency and thetemperature. The temperature may also be inferred by measuring thedeflection of the cantilever before and after turning the light beam on(or off).

Frequency-modulated AFM (FM-AFM) imaging has garnered a great deal ofattention because of its high spatial resolution in air, vacuum and evenfluid. Even with the prior art, FM-AFM has demonstrated success atimaging single atomic defects, imaging individual chemical bonds betweensurface atoms and measuring the force as a single atom was moved acrossa surface.

FM-AFM also permits simultaneous measurement of dissipative interactionsbetween the tip of the cantilever and the sample. Dissipation is acombined effect of multiple interactions including long rangeelectrostatic and magnetic interactions, as well as hystereticinteratomic forces associated with the approach and retraction of thetip of the cantilever from the surface. In the prior art the measurementof dissipation has been unreliable. Dissipation is difficult to quantifyand relate to underlying physical mechanisms and results have not beenreproducible. One important feature required for accurate dissipationmeasurements is frequency independent probe excitation. Specifically,coupling between the drive amplitude and frequency can lead to spuriousdissipation measurements. Piezoacoustic excitation, especially inliquid, suffers from a “forest of peaks” in the transfer functionbetween the excitation voltage and the mechanical motion. These peaksare caused by spurious resonances in the mechanical system, such as theresonances of a cantilever holder or liquid droplet. The peaks are notreproducible from one experiment to the next, and can even drift duringone experiment. Because of these peaks, piezoacoustic excitation is veryfrequency-dependent, sometimes changing by a factor of ten within theprobe bandwidth. Since the photothermal drive described here issubstantially constant or at the least varies only slowly over typicaloperational frequencies, it provides more accurate dissipationmeasurements than the piezoacoustic excitation commonly used in theprior art and is much more reproducible.

blueClean

After what is usually substantial use, AFM probes become contaminated byinteraction with the sample. Contaminated probes must either be replacedby new probes or where feasible cleaned. In typical laboratory settings,probes are often cleaned ex situ using an assortment of chemicalsolutions, sometimes combined with UV exposure. In prior art, adedicated apparatus was often used for cleaning probes. The cleaning ofprobes frequently involves a significant amount of time, and often isnot successful. However replacing a contaminated probe with a new onecan cost a significant amount of money. In either case, the experimentmust be halted to remove and replace the existing probe from the AFM.Removing and replacing the probe also loses information regarding thesample location being imaged.

Heating the probe may be used as a method of cleaning the tip of thecantilever. For this purpose light at the blue end of the visiblespectrum is preferred. The inventors have used the beam from a laseremitting light with a wave length of 405 nm with satisfactory results.

Before, during, or after imaging a sample, the light beam of an opticalbeam positioning unit may be turned on momentarily to heat the tip ofthe cantilever in order to modify the tip coating or to break down,thermally modify or remove contaminations that have adhered to the tip.This method of cleaning or modifying the tip of the cantilever has theadvantage over prior art that the process can be performed in situ,while the probe is in close proximity to the sample. The fact that thetip of the cantilever can be cleaned or modified without removing itfrom the AFM is a time-saving and important improvement in that itallows the continuation of the experiment after cleaning or modificationwithout any cumbersome repositioning of the probe.

A well-parameterized probe is very important in nanomechanicalmeasurements, such as stiffness, storage and loss moduli, loss tangents,adhesion, indentation and a host of other parameters known to oneskilled in the art. For this application a clean probe is of greatimportance.

Sample Modification

The light beam of an optical beam positioning unit may be used forinducing photochemical, photovoltaic, photothermal, pyroelectric orother light sensitive changes to specific portions of the sample. Forphotothermal changes light at the blue end of the visible spectrum ispreferred. The inventors have used the beam from a laser emitting lightwith a wave length of 405 nm with satisfactory results. Forphotochemical, photovoltaic and pyroelectric changes light with avariety of wave lengths is satisfactory.

Changes of this character may be accomplished either with the beampositioned on the probe or with the beam off the probe. The positioningof the light beam allows the user to select the locations of the samplethat may undergo such changes, while the total power of the light beamcan be tuned to vary the degree of changes induced in the chosen samplelocation. Moving the position of the focused light beam in two or threedimensions while varying the light power of the light beam enables thepreparation or modification of the AFM sample before, during, or afterimaging.

blueTracking

As discussed above, in an AFM changes in the oscillation amplitude ofthe probe are typically made to trigger a change in the verticalposition of the base of the probe relative to the sample (referred toherein as a change in the Z position, where Z is generally orthogonal tothe X/Y plane defined by the sample), in order to maintain theoscillation amplitude at a constant pre-set value. It is this feedbackthat is typically used to generate an AFM image as the probe is rasteredabove the sample surface.

In some instances however mechanical resonances of the AFM hardwarelimit the response time of tracking the Z position of the sampletopography. Attempting to track the surface of the sample with afrequency bandwidth that exceeds these mechanical resonances leads tooscillations that prevent accurate topography tracking and damage thetip of the cantilever.

This issue can be avoided by using the light beam to induce deliberatesub-resonance bending of the cantilever. Bending a cantilever upwards ordownwards is analogous to moving the sample downwards or upwards.Because the mechanical resonance of a small cantilever greatly exceedsthe mechanical resonance of the AFM mechanical hardware, the feedbackfor keeping constant oscillation amplitude for accurate topographytracking can be operated at very high frequencies—upwards of 100 kHz.

For this purpose light at the blue end of the visible spectrum ispreferred. The inventors have used the beam from a laser emitting lightwith a wave length of 405 nm on a gold coated cantilever withsatisfactory results. Other wavelengths may be preferable if thecantilever is uncoated or coated with a material other than gold.

By varying the light power at time scales slower than the oscillationperiod of the cantilever, the cantilever bending can be approximated aslinear with the light power. The light power is thus used to change thedistance between the tip of the cantilever and the sample in order totrack topography changes while rastering the tip over the samplesurface. This device for tracking topography changes can be used inconjunction with the optical lever of an AFM, or can entirely replacethe optical lever. In other words, as the sample is moved in the x and ydirection for scanning, the cantilever bending resulting from the use oflight power changes can be used to maintain the conditions fortopography tracking. For example, in the case of amplitude modulatedAFM, the on-resonance amplitude of oscillation can be held constant bythe aid of a feedback loop that changes the cantilever bending throughthe use of light power changes. This method has the additional advantagethat the same light beam can be used to oscillate the cantilever onresonance while the average light power is independently modulated totrack the sample topography.

Although only a few embodiments have been disclosed in detail above,other embodiments are possible and the inventors intend these to beencompassed within this specification. The specification describesspecific examples to accomplish a more general goal that may beaccomplished in another way. This disclosure is intended to beexemplary, and the claims are intended to cover any modification oralternative which might be predictable to a person having ordinary skillin the art. For example, other devices, and forms of modularity, can beused.

Also the inventors intend that only those claims which use the words“means for” are intended to be interpreted under 35 USC 112, sixthparagraph. Moreover, no limitations from the specification are intendedto be read into any claims, unless those limitations are expresslyincluded in the claims. The computers described herein may be any kindof computer, either general purpose, or some specific purpose computersuch as a workstation. The computer may be a Pentium class computer,running Windows XP or Linux, or may be a Macintosh computer. Thecomputer may also be a handheld computer, such as a PDA, cellphone, orlaptop.

The programs may be written in C, or Java, Brew or any other programminglanguage. The programs may be resident on a storage medium, e.g.,magnetic or optical, e.g. the computer hard drive, a removable disk ormedia such as a memory stick or SD media, or other removable medium. Theprograms may also be run over a network, for example, with a server orother machine sending signals to the local machine, which allows thelocal machine to carry out the operations described herein.

What is claimed is:
 1. An atomic force microscope system that operatesto characterize a piezoelectric sample, comprising: an atomic forcemicroscope probe having a cantilever with a cantilever tip; thecantilever tip in contact with the piezoelectric sample, a bias voltagesource, producing a bias voltage between the cantilever tip and thepiezoelectric sample, the bias voltage source modulating the biasvoltage periodically to generate an oscillating electric field below thecantilever tip, which leads to localized deformations in a surface ofthe sample, which deformations act as a mechanical drive for thecantilever tip; a controller which determines a contact resonancefrequency of the cantilever tip on the sample; and a tip amplitudedetector which measures a magnitude of effective piezoelectric responseof the surface, as an amplitude of a tip displacement divided by anamplitude of the bias voltage between the tip and sample, where the tipamplitude detector measures the response at a spot on the cantilever,and where a location of the spot on the cantilever is adjustable, andwhere the tip amplitude detector optimizes the spot by adjusting thelocation using iterative minimization of the measured frequency responsearound the resonance frequency.
 2. The system as in claim 1, wherein thecontroller operates at only a single frequency of oscillating electricfield.
 3. The system as in claim 1, wherein a phase of the effectivepiezoelectric response of the surface provides information about apolarization direction.
 4. The system as in claim 1, wherein the spot isa laser spot.
 5. The system as in claim 4, wherein the spot is a laserspot from a laser Doppler vibratometer.
 6. The system as in claim 4,where the tip amplitude detector optimizes the spot by adjusting thelocation using iterative minimization until achieving a flat frequencyresponse around the contact resonance.
 7. The system as in claim 4,wherein the oscillating electric field is in the Mhz range.
 8. An atomicforce microscope system that operates to characterize a piezoelectricsample, comprising: an atomic force microscope probe having a cantileverwith a cantilever tip; the cantilever tip in contact with thepiezoelectric sample, a bias voltage source, producing a bias voltagebetween the cantilever tip and the piezoelectric sample, the biasvoltage source modulating the bias voltage periodically to generate anoscillating electric field below the cantilever tip, which leads tolocalized deformations in a surface of the sample, which deformationsact as a mechanical drive for the cantilever tip; a controller whichdetermines a contact resonance frequency of the cantilever tip on thesample; and a tip amplitude detector which measures a magnitude ofeffective piezoelectric response of the surface, as an amplitude of atip displacement divided by an amplitude of the bias voltage between thetip and sample, where the tip amplitude detector measures the responseat a spot on the cantilever, and where a location of the spot on thecantilever is adjustable, and where the tip amplitude detector optimizesthe spot by adjusting the location using iterative minimization of themeasured frequency response around the resonance frequency to place thespot on the cantilever directly over the cantilever tip.
 9. The systemas in claim 8, wherein the controller operates at only a singlefrequency of oscillating electric field.
 10. The system as in claim 8,wherein a phase of the effective piezoelectric response of the surfaceprovides information about a polarization direction.
 11. The system asin claim 8, wherein the spot is a laser spot.
 12. The system as in claim8, wherein the spot is a laser spot from a laser Doppler vibratometer.13. The system as in claim 8, where the tip amplitude detector optimizesthe spot by adjusting the location using iterative minimization untilachieving a flat frequency response around the contact resonance. 14.The system as in claim 8, wherein the oscillating electric field is inthe Mhz range.